Let f(x)=25x^2+kx+2,where k is real.

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Let f(x)=25x^2+kx+2,where k is real.
(a) If f(x)=0 has equal roots,find the value(s) of k,leaving your answer(s) in simplest surd form.(3marks)
(b) If a is the smaller positive root of the quadratic equation f(x)=0,and one root is half of the other,express,in term of a,
(i) the larger root,
(ii) the product of the roots.
Hence find the roots of the equation and the value of k.(5marks)

(a) f(x)=25x^2+kx+2=0 has equal roots
delta=k^2-4*25*2=0 k=±10√2
(b) one root is half of the other
hence the larger root is double of the smaller root a
(i) 2a
(ii) 2a^2
a*2a=2/25
a is positive
a=1/5 2a=2/5
1/5+2/5=-k/25
k=-15
the two roots are 1/5 and 2/5
k is -15

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